Project 3:
All Things Cryptography
Project Files and PDF/docx Templates:
You can download a zip file with the starter files here.
Goals of the Project:
● Understand and advance their knowledge of cryptography and hashing
● Understanding how these are implemented by working through examples
● Understanding how and why the exploit could be completed on vulnerable systems
Information:
Before starting, make SURE you are using Python VERSION 3.7.x OR LOWER. Version 3.8 includes
some functionality that may not be compatible with the autograder environment, which runs Python
Version 3.6.7. To check your version of Python, open a command prompt and run the command:
python –version
For the established algorithms that you may need to use, you are allowed to reference and implement
pseudocode with PROPER CITATION. What is Pseudocode? https://en.wikipedia.org/wiki/Pseudocode
UNDER NO CIRCUMSTANCES should you copy/paste code into the project. Doing so is an honor code
violation (not to mention a real world security concern) and will result in a zero (Refer to syllabus for
more information).
The final deliverables:
You will submit gt_user_id_project3.pdf in 2 places.
n = int(n_str, 16)
d = int(d_str, 16)
c = int(c_str, 16)
m = 0
return hex(m).rstrip(‘L’)
2
GT CS 6035: Introduction to Information Security
Task 2 – Warm-up, Get Familiar with Hashes (7 points)
By now we’ve learned that hashes are one-way functions. Because of this unique feature,
passwords are often stored as hashes in order to protect them from prying eyes. Even if a hacker
infiltrated our state-of-the-art Georgia Tech security systems, he or she would not be able to derive
the plaintext passwords from the hashes. But what if we made the critical mistake of using a
common password? How safe would we be?
Let’s find out…
You are given a list of some of the most commonly-used passwords on the Internet. You are also
given the SHA256 hash of a password randomly selected from this list. Your job is to discover the
plaintext password behind the hash.
The complete list of common passwords is pre-loaded for you in project_3.py.
TODO: In the provided project_3.py file, implement the stub method task_2.
def task_2(self, password_hash: str) -> str:
password = common_password_list[0]
hashed_password = hashlib.sha256(password.encode()).hexdigest()
return password
Reflection
In a maximum of 200 words, address the following prompt:
● Knowing that a lot of people like to use these common passwords, make one suggestion
for how you could implement improved password security.
3
GT CS 6035: Introduction to Information Security
Task 3 – Kernelcoin Part 1 (9 points)
Background: A blockchain is a distributed, immutable ledger that derives its security, in part, from a
chain of cryptographic hash values. For more detail, please read Section II of Hassan et al.,
Blockchain and the Future of the Internet: A Comprehensive Review, arXiv:1904.00733v1 (23 Feb.
2019), available online at: https://arxiv.org/pdf/1904.00733.pdf.
Today is your lucky day! You’ve discovered a brand new cryptocurrency called Kernelcoin (symbol:
RTI). There are rumors that Costco will soon announce Kernelcoin as the preferred payment
method in its warehouse stores. This news is sure to send the price of Kernelcoin to the moon, and
Kernelcoin holders to the nearest Lamborghini dealership.
You plan to start mining Kernelcoin so that you can earn even more. In order to do so, you need to
create a valid block to append to the previous block. A valid block contains the lowest nonce value
that, when concatenated with the transaction string, and the hash of the previous block (in that
order, i.e. nonce + transaction string + previous block hash), will produce a SHA256 hash with two
leading zeros (the proof-of-work for this particular blockchain). Transaction strings have the syntax
“UserID1:UserID2:X”, indicating that UserID1has transferred X Kernelcoin to UserID2. You are given
all of these values, and your goal is to find the lowest possible nonce value for the resulting block.
TODO: In the provided project_3.py file, implement the method task_3.
def task_3(self, user_id_1: str, user_id_2: str, amount: int, prev_block_hash:
str) -> int:
nonce = 0
return nonce
Reflection
In a maximum of 200 words, address the following prompt:
The kernelcoin blockchain uses a proof-of-work scheme as a consensus mechanism (i.e., finding a
hash with a certain number of leading zeros).
● Name and briefly explain an alternative consensus mechanism.
● List its strengths and weaknesses compared to proof-of-work.
4
GT CS 6035: Introduction to Information Security
Task 4 – Kernelcoin Part 2 (9 points)
Sure enough, once /r/WallStreetBets found out about Kernelcoin the price rose to nosebleed levels.
The Kernelcoin that you mined is now worth a fortune! Feeling generous, you decide to donate a
small portion of your gains to Georgia Tech so that the school can give its TAs a much-deserved
raise. As you prepare to send the transaction, you start to wonder how Kernelcoin verifies that
transactions are valid…
After doing some research you find that a Kernelcoin transaction is hashed and encrypted with
your private key to create a digital signature. This signature is broadcast to the network along with
the original transaction string. If the signature checks out, then the transaction is a candidate for
inclusion in the next block.
TODO: In the provided project_3.py file, finish the code for signing a Kernelcoin transaction in
the method task_4. (You may find the code that you wrote in Task 1 helpful for this.)
def task_4(self, from_user_id: str, to_user_id: str, amount: int, d: int, e: int,
n: int) -> int:
return signature
Reflection
In a maximum of 200 words, address the following prompt:
Imagine that you are coding a function that accepts a Kernelcoin transaction string and a digital
signature. The public address of the signer is also passed to the function. The purpose of the
function is to verify the validity of the transaction (i.e. it returns a boolean value).
● Explain the high-level steps necessary to implement this function. No code is required. You
should use your own words.
5
GT CS 6035: Introduction to Information Security
Task 5 – Attack A Small Key Space (15 points)
The algorithm you search for is dirt simple which makes it hard for attackers to traverse the entire
key space with limited resources. Now, you’re given a unique RSA public key with a relatively small
key size (64 bits).
Your goal is to get the private key.
TODO: In the provided project_3.py file, implement the method get_factors. 𝑛 is the given
public key, and your goal is to get its factors.
def get_factors(self, n: int):
p = 0
q = 0
return p, q
TODO: In the provided project_3.py file, implement the method
get_private_key_from_p_q_e to get the private key.
def get_private_key_from_p_q_e(self, p: int, q: int, e: int):
d = 0
return d
Reflection
In a maximum of 500 words, address the following prompts:
Explain in your own words how you were able to get the private key.
● What were the steps you followed?
● What was the underlying mathematical principle?
6
GT CS 6035: Introduction to Information Security
Task 6 – Where’s Waldo (25 Points)
Read the paper “Mining Your Ps and Qs: Detection of Widespread Weak Keys in Network Devices”,
which can be found at: https://factorable.net/weakkeys12.extended.pdf. You will not be able to
understand the purpose of this task nor write about it properly in your essay unless you read the
entire paper. Do not skip it, do not skim it, read the whole of it.
You are given a unique RSA public key, but the RNG (random number generator) used in the key
generation suffers from a vulnerability described in the paper above. In addition, you are given a list
of public keys that were generated by the same RNG on the same system. Your goal is to get the
unique private key from your given public key using only the provided information.
TODO: In the provided project_3.py file, implement the method task_6. (More information
about Waldo, and why everyone keeps looking for him can be found here:
https://en.wikipedia.org/wiki/Where%27s_Wally%3F. Knowledge of “Where’s Waldo?” isn’t strictly
necessary to solve this task, but it might give you a nudge in the right direction…)
def task_6(self,
given_public_key_n: int,
given_public_key_e: int,
public_key_list: list) -> int:
d = 0
return d
Reflection
In a maximum of 500 words, address the following prompts:
● Why is the public key used in this task vulnerable? Explain this in your own words. Please
talk about the potential problems with the key generation and the associated mathematical
principles in your answer.
● What steps did you take to derive the private key result in this task? Please discuss the
underlying mathematical principles at a high level and explain how you arrived at your
answer.
7
GT CS 6035: Introduction to Information Security
Task 7 – Broadcast RSA Attack (30 Points)
A message was encrypted with three different 1,024-bit RSA public keys, resulting in three different
encrypted messages. All of them have the public exponent 𝑒 = 3.
You are given the three pairs of public keys and associated encrypted messages. Your job is to
recover the original message.
TODO: In the provided project_3.py file, implement the method task_7.
def task_7(self,
n_1_str: str, c_1_str: str,
n_2_str: str, c_2_str: str,
n_3_str: str, c_3_str: str) -> str:
n_1 = int(n_1_str, 16)
c_1 = int(c_1_str, 16)
n_2 = int(n_2_str, 16)
c_2 = int(c_2_str, 16)
n_3 = int(n_3_str, 16)
c_3 = int(c_3_str, 16)
msg = ”
m = 0
msg = bytes.fromhex(hex(m).rstrip(‘L’)[2:]).decode(‘UTF-8’)
return msg
Reflection
In a maximum of 500 words, address the following prompts:
● How does the broadcast RSA attack work?
● What causes the vulnerability?
● Explain this in your own words and explain at a high level the mathematical principles
behind it.
● Explain how you recovered the message, ensuring that you give thorough detail on all of
your steps.
Sample Solution